If $A=\{1,2,3,4\}$  and $f:A\to A$  is defined by  $f=\{(1,3),(2,4),(3,2),(4,1)\}$, then  is given by
 

$Givenf=\left\{\left(1,3\right),\left(2,4\right)\left(3,2\right),\left(4,1\right)\right\}$

$\therefore fof=\left\{\left(1,2\right),\left(2,1\right)\left(3,4\right),\left(4,3\right)\right\}$

$\therefore fofofof=\left\{\left(1,1\right),\left(2,2\right)\left(3,3\right),\left(4,4\right)\right\}$

$\underset{2012times}{\underbrace{fofofo\mathrm{.........}of\left(x\right)}}$$=\left\{\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right)\right\}$